A radar and a jammer are considered as informed opponents "playing" in a noncooperative two-player, zero-sum game. The effects of jamming on the target detection performance of a radar using constant false alarm rate (CFAR) processing are analyzed using a game theoretic approach for three cases: 1) ungated range noise (URN), 2) range-gated noise (RGN) and 3) false-target (FT) jamming. Assuming a Swerling type II target in the presence of Rayleigh-distributed clutter, utility functions are described for cell-averaging (CA) and order statistic (OS) CFAR processors and the three cases of jamming. The analyses included optimizations of these utility functions subject to certain constraints with respect to control variables (strategies) in the jammer such as jammer power and the spatial extent of jamming and control variables in the radar such as threshold parameter and reference window size. The utility functions are evaluated over the players' strategy sets, and the resulting matrix-form games are solved for the optimal or "best response" strategies of both the jammer and the radar.